Dependence of the Drag Over Super Hydrophobic and Liquid Infused Surfaces on the Textured Surface and Weber Number

Direct Numerical Simulations of a turbulent channel flow have been performed. The lower wall of the channel is made of staggered cubes with a second fluid locked in the cavities. Two viscosity ratios have been considered, m = μ 1 / μ 2 = 0.02 and 0.4 (the subscript 1 indicates the fluid in the cavities and 2 the overlying fluid) mimicking the viscosity ratio in super–hydrophobic surfaces (SHS) and liquid infused surfaces (LIS) respectively. A first set of simulations with a slippery interface has been performed and results agree well with those in literature for perfect slip conditions and Stokes approximations. To assess how the dynamics of the interface affects the drag, a second set of DNS has been carried out at W e = 40 and 400 corresponding to W e + ≃ 1 0 − 3 and 1 0 − 2 . The deformation of the interface is fully coupled to the Navier-Stokes equation and tracked in time using a Level Set Method. Two gas fractions, GF = 0.5 and 0.875, have been considered to assess how the spacing between the cubes affects the deformation of the interface and therefore the drag. For the dimensions of the substrate here considered, under the ideal assumption of flat interface, staggered cubes with GF = 0.875 provide about 20 % drag reduction for W e = 0 . However, a rapid degradation of the performances is observed when the dynamics of the interface is considered, and the same geometry increases the drag of about 40 % with respect to a smooth wall. On the other hand, the detrimental effect of the dynamics of the interface is much weaker for GF = 0.5 because of the reduced pitch between the cubes.